Answered: Random and independent samples of 90…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Random and independent samples of 90 recent primetime airings from each of the two major networks have been considered. The first network aired a mean of 110.7 commercials during prime time, with a standard deviation of 4.3 commercials. The second network aired a mean of 109.3 commercials, with standard deviations of 4.6 commercials. As the sample sizes are quite large, the population standard deviation can be estimated using the sample standard deviation. Construct a 95% confidence interval for u1 -u2, the difference between the mean number of commercial u1 aired during prime time by the first network and the mean number of commercials u2 aired during prime time by the second network. Then find the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answer to at least two decimals places. Lower limit: Upper limit:

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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